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# A certain company sells jellybeans in the following six flavors only

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Intern
Joined: 30 Mar 2017
Posts: 2
Location: India
Concentration: Finance, General Management
A certain company sells jellybeans in the following six flavors only [#permalink]

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16 Sep 2017, 11:01
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Difficulty:

75% (hard)

Question Stats:

59% (01:39) correct 41% (03:11) wrong based on 41 sessions

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A certain company sells jellybeans in the following six flavors only: b, c, g, l, p, s. If the jellybeans are sorted randomly into boxes containing exactly 2, 3, 4 different flavors only, what is the probability that any given box contain g jellybeans?

A 1/6
B 1/3
C 2/5
D 1/2
E 3/4

[Reveal] Spoiler: OA
Manager
Joined: 27 Dec 2016
Posts: 233
Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Re: A certain company sells jellybeans in the following six flavors only [#permalink]

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16 Sep 2017, 11:47
vinay888 wrote:
A certain company sells jellybeans in the following six flavors only: b, c, g, l, p, s. If the jellybeans are sorted randomly into boxes containing exactly 2, 3, 4 different flavors only, what is the probability that any given box contain g jellybeans?

A 1/6
B 1/3
C 2/5
D 1/2
E 3/4

First, I think it is easier to calculate the denominator first.
- Total outcomes in box with 2 different flavor : 6C2 = 15
- Total outcomes in box with 3 different flavor : 6C3 = 20
- Total outcomes in box with 4 different flavor : 6C4 = 15
- Total all possible outcomes = 50.

Now, we can find the numerator.
- We can calculate probability of AT LEAST G in each boxes with : 1 - probability NO G in each boxes.
- Total outcomes WITHOUT G in box with 2 different flavor : 5C2 = 10
- Total outcomes WITHOUT G in box with 3 different flavor : 5C3 = 10
- Total outcomes WITHOUT G in box with 4 different flavor : 5C4 = 5
- Total outcomes WITHOUT G = 25, so total outcome AT LEAST G in each boxes = 50-25 = 25.

Probability = $$\frac{25}{50}$$ or $$\frac{1}{2}$$.

Wdyt?
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Re: A certain company sells jellybeans in the following six flavors only   [#permalink] 16 Sep 2017, 11:47
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